Dirac Delta

Evaluate the Dirac delta function.

The Dirac delta function may be loosely defined as

delta equals StartLayout Enlarged left-brace 1st Row 1st Column normal infinity 2nd Column if x equals 0 2nd Row 1st Column 0 2nd Column if x not-equals 0 EndLayout

and is constrained to satisfy the identity

integral Subscript negative normal infinity Superscript plus normal infinity Baseline delta left-parenthesis x right-parenthesis d x equals 1

Note that the Dirac delta function is not a function in the traditional sense, as any real-valued function which is zero everywhere except at a single point, must have an integral equal to 0.

Usage

var diracDelta = require( '@stdlib/math/base/special/dirac-delta' );

diracDelta( x )

Evaluates the Dirac delta function.

var v = diracDelta( 0.0 );
// returns Infinity

v = diracDelta( 3.14 );
// returns 0.0

v = diracDelta( NaN );
// returns NaN

Examples

var linspace = require( '@stdlib/math/utils/linspace' );
var diracDelta = require( '@stdlib/math/base/special/dirac-delta' );

var x = linspace( -1.0, 1.0, 101 );
var i;

for ( i = 0; i < x.length; i++ ) {
    console.log( 'dirac(%d) = %d', x[ i ], diracDelta( x[ i ] ) );
}